Simplify the following expression and state the condition under which the simplification is valid. $r = \dfrac{p^2 - 4}{p - 2}$
Explanation: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = p$ $ b = \sqrt{4} = -2$ So we can rewrite the expression as: $r = \dfrac{({p} {-2})({p} + {2})} {p - 2} $ We can divide the numerator and denominator by $(p - 2)$ on condition that $p \neq 2$ Therefore $r = p + 2; p \neq 2$